Optical beam scanning device and image forming apparatus

ABSTRACT

It is an object of the present invention to provide an optical beam scanning device and an image forming apparatus which suppress displacement of plural images formed by a different photoconductor in a sub-scanning direction by means of a simple structure even if temperature changes. The optical beam scanning device of the present invention has a single light deflecting device, a pre-deflection optical system that allows light beams from a plurality of light sources to enter the light deflecting device, and a post-deflection optical system including a first optical element for imaging reflected light beams from the light deflecting device on surfaces to be scanned for respective light beams. A second optical element, which has a positive or negative power opposite to a power of the first optical element in a sub-scanning direction, is provided in a position of the pre-deflection optical system where the light beams passes commonly and the light beams enter with distance in the sub-scanning direction. The image forming apparatus of the present invention has the optical beam scanning device of the present invention.

The present application is a divisional of U.S. application Ser. No.11/049,973, filed Feb. 4, 2005, the entire contents of which isincorporated herein by reference.

BACKGROUND OF THE INVENTION

The invention relates to an image forming apparatus such as a laserprinter and a digital copying machine, and an optical beam scanningdevice that can be used in the image forming apparatus.

For example, a color image forming apparatus of plural drum type isconstituted so that a plurality of images are created on photoconductordrums, the images are overlapped with one another on a recording medium,and one image is formed. The apparatus utilizes a plurality of imageforming sections corresponding to separated color components, and anoptical beam scanning device (laser exposing device). The optical beamscanning device provides image data corresponding to the colorcomponents, namely, a plurality of laser beams to the image formingsections.

In such a color image forming apparatus, it is necessary to suitablyestablish a positional relationship of the images on the photoconductordrums, particularly the positional relationship in a sub-scanningdirection in order to realize a color image without color shift (colorregistration error) A lot of optical elements, however, intervenebetween light sources and the photoconductor drums, and the opticalelements are influenced by ambient temperature and humidity, therebyoccasionally causing color shift.

In order to suppress the color shift in the sub-scanning direction(displacement between the color component images), the method disclosedin U.S. Pat. No. 6,337,757 is proposed.

In this method, pre-deflection optical systems for respective colorcomponents, which are provided between light sources for the colorcomponents and a deflector shared by the color components, are providedwith a hybrid cylinder lens. The hybrid cylinder lens is composed of aglass cylinder lens having a positive power in the sub-scanningdirection through which light beams transmit with eccentricity and tilt,and a plastic cylinder lens having a negative power in the sub-scanningdirection. As a result, displacement in the sub-scanning direction dueto a change in the ambient temperature is suppressed for each colorcomponent.

In the above conventional method, however, the plastic cylinder lensshould be provided for each color component (when the color componentsare yellow, magenta, cyan and black, four plastic cylinder lenses),thereby making the apparatus complicated and expensive.

When the hybrid cylinder lens is moved to an optical axial direction forfocus adjustment that focuses the beams on image surfaces (surfaces ofthe photoconductor drums), the hybrid cylinder lens allows the lightbeams to transmit with eccentricity and tilt. For this reason, emittingpositions on the image surfaces (beam positions) are changed.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an optical beamscanning device and an image forming apparatus that are capable ofcompensating a shift of beam positions of images in a sub-scanningdirection caused by a change in use environment by simple structure andsuppressing the displacement between the images.

A first aspect of the invention is an optical beam scanning deviceincluding: a single light deflecting device; a pre-deflection opticalsystem that allows light beams from a plurality of light sources toenter the light deflecting device; and a post-deflection optical systemincluding a first optical element for imaging the reflected light beamsfrom the light deflecting device on surfaces to be scanned for therespective light beams, characterized in that a second optical elementhaving a positive or negative power opposite to a power of the firstoptical element in a sub-scanning direction is provided in a position ofthe pre-deflection optical system which allows the light beams from thelight sources to pass therethrough and allows the light beams from thelight sources to enter in the sub-scanning direction with distance.

A second aspect of the invention is an optical beam scanning devicecharacterized by including a plurality of optical elements that arearranged on a housing and give a plurality of scanning lines to aplurality of photoconductor with an internal L, wherein linear expansioncoefficients of the housing, a frame for locating the photoconductor anda shaft for driving a belt on which images developed on thephotoconductor drums are overlapped are designated by αH, αF and αS,respectively, and when an interval between the beams positions onsurfaces to be scanned in a sub-scanning direction at the time ofdeveloping an optical path reflection from a deflecting surface to thesurfaces to be scanned is designated by BP, characteristics ofcomponents are selected so that positions of the beams in thesub-scanning direction are shifted only by −(αH−2×αF+αS)×L+αH×BP perunit temperature.

A third aspect of the invention is an optical beam scanning devicecharacterized by including: a single light deflecting device; apre-deflection optical system that allows light beams from a pluralityof light sources to enter the light deflecting device; and apost-deflection optical system including a first optical element forimaging reflecting light beams from the light deflecting device onsurfaces to be scanned for respective light beams, whereincharacteristics of components including the light deflecting device, thepre-deflection optical system and the post-deflection optical system areselected so that intervals of the light beams from the light sources onthe surfaces to be scanned at the time of developing an optical pathreflection from a deflecting surface to the surfaces to be scannedbecome small when temperature rises.

According to the optical beam scanning device and the image formingapparatus of the present invention, even when ambient environment suchas temperature changes, displacement of the images formed by differentphotoconductor drums in the sub-scanning direction can be suppressed bya simple structure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic sectional view illustrating an image formingapparatus that uses a multi-beam optical scanning device according to anembodiment;

FIG. 2 is a schematic plan view illustrating an arrangement of opticalmembers in the optical beam scanning device incorporated into the imageforming apparatus of FIG. 1;

FIG. 3 is a schematic sectional view explaining a state that areflecting point of a light deflecting device and a center of apost-deflection optical system in a scanning direction are cut in theoptical beam scanning device of FIG. 2;

FIGS. 4A and 4B are explanatory diagrams illustrating functions of anenvironment change compensating optical element 15;

FIG. 5 is an explanatory diagram illustrating a normal state of variousparameters influenced by temperature change;

FIG. 6 is an explanatory diagram illustrating an influence of afluctuation in scanning line positions (laser beam emitting positions);

FIG. 7 is an explanatory diagram illustrating an influence of afluctuation in positions of photoconductor drums;

FIG. 8 is a chart illustrating curvature, interval, refractive index ofrespective optical elements, and the like on an optical axis on eachsurface of the optical elements according to a first concrete example ofthe embodiment;

FIG. 9 is a chart illustrating eccentricity and tilt amount of theoptical elements according to the first concrete example of theembodiment;

FIGS. 10A to 10F are charts illustrating curved surface polynomialcoefficient of each surface of each optical element according to thefirst concrete example of the embodiment;

FIG. 11 is a chart illustrating a paraxial power characteristic of theenvironment change compensating optical element 15 according to thefirst concrete example of the embodiment;

FIG. 12 is a chart illustrating a change of the positions whentemperature rises by 15° C. according to the first concrete example ofthe embodiment;

FIG. 13 is a chart illustrating curvature, interval, refractive index ofthe respective optical elements on the optical axis on the surfaces ofthe optical elements according to a second concrete example of theembodiment;

FIG. 14 is a chart illustrating eccentricity and tilt amount of theoptical elements according to the second concrete example of theembodiment;

FIGS. 15A and 15B are charts illustrating curved surface polynomialcoefficient of each surface of each optical element according to thesecond concrete example of the embodiment;

FIG. 16 is a chart illustrating a paraxial power characteristic of theenvironment change compensating optical element 15 according to thesecond concrete example of the embodiment;

FIG. 17 is a chart illustrating a change of the positions whentemperature rises by 15° C. according to the second concrete example ofthe embodiment;

FIG. 18 is a chart illustrating curvature, interval, refractive index ofthe respective optical elements on the optical axis on the surfaces ofthe optical elements according to a comparative example of theembodiment;

FIG. 19 is a chart illustrating eccentricity and tilt amount of theoptical elements according to the comparative example of the embodiment;

FIG. 20 is a chart illustrating a paraxial power characteristic of theenvironment change compensating optical element 15 according to thecomparative example of the embodiment; and

FIG. 21 is a chart illustrating a change of the positions whentemperature rises by 15° C. according to the comparative example of theembodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

An optical beam scanning device and an image forming apparatus accordingto preferable embodiments of the present invention are explained belowwith reference to the drawings.

(A) One Embodiment

The optical beam scanning device and the image forming apparatusaccording to one embodiment of the present invention will be explained.The optical beam scanning device according to the embodiment is amulti-beam optical scanning device.

FIG. 1 illustrates a color image forming apparatus that uses themulti-beam optical scanning device according to the embodiment. In thiskinds of the color image forming apparatus, four sets of four image datain which a color is separated into respective components of yellow (Y),magenta (M), cyan (C) and black (B) (black is for inking), and variousdevices which form images for the respective color componentscorrespondingly to Y, M, C and B are normally used. For this reason, inthe following explanation and the drawings, Y, M, C and B are added tothe reference numerals, so that the image data for the respective colorcomponents and the devices corresponding to them are identified.

In FIG. 1, an image forming apparatus 100 has first through fourth imageforming sections 50Y, 50M, 50C and 50B that form images for separatedcolors: yellow; magenta; cyan; and black.

The image forming sections 50Y, 50M, 50C and 50B are arranged in seriesin this order below the optical beam scanning device 1 correspondinglyto positions from which laser beams L (Y, M, C and B) corresponding tothe images of the color components are emitted via third reflectingmirrors 37Y, 37M and 37C, and first reflecting mirror 33B of amulti-beam optical scanning device 1, mentioned later, with reference toFIGS. 2 and 3.

A transport belt 52, which transports a transfer material (recordingmedium) to which images formed by the image forming sections 50 (Y, M, Cand B) are transferred, is arranged below the respective image formingsections 50 (Y, M, C and B).

The transport belt 52 is bridged between a belt driving roller 56 and atension roller 54 which rotate to a direction of an arrow by a motor,not shown. The transport belt 52 is rotated at a predetermined speed toa direction where the belt driving roller 56 rotates, and moves straightbelow the image forming sections 50 (Y, M, C and B).

The image forming sections 50 (Y, M, C and B) have photoconductor drums58Y, 58M, 58C and 58B having a cylindrical drum shape and are formedrotatively to a clockwise direction in FIG. 1. Electrostatic latentimages corresponding to the images are formed on the photoconductordrums 58Y, 58M, 58C and 58B, respectively.

Charging devices 60Y, 60M, 60C and 60B, developing devices 62Y, 62M, 62Cand 62B, transfer devices 64Y, 64M, 64C and 64B, cleaners 66Y, 66M, 66Cand 66B, and discharging devices 68Y, 68M, 68C and 68B are arrangedaround the photoconductor drums 58 (Y, M, C and B), respectively, inthis order along the rotational direction of the photoconductor drums 58(Y, M, C and B). The charging devices 60 (Y, M, C and B) apply apredetermined electric potential to the surfaces of the photoconductordrums 58 (Y, M, C and B). The developing devices 62 (Y, M, C and B)supply toner with colors corresponding to the electrostatic latentimages formed on the surfaces of the photoconductor drums 58 (Y, M, Cand B) so as to develop the images. The transfer devices 64 (Y, M, C andB) are opposed to the photoconductor drums 58 (Y, M, C and B) with thetransport belt 52 intervening between the transfer devices 64 and thephotoconductor drums 58 (Y, M, C and B), and transfer the toner imageson the photoconductor drums 58 (Y, M, C and B) onto the transport belt52 or a recording medium, namely, a recording paper P transported bymeans of the transport belt 52. The cleaners 66 (Y, M, C and B) removeresidual toner on the photoconductor drums 58 (Y, M, C and B) after thetoner images are transferred by the transfer devices 64 (Y, M, C and B).The discharging devices 68 (Y, M, C and B) eliminate residual potentialon the photoconductor drums 58 (Y, M, C and B) after the toner imagesare transferred by the transfer devices 64 (Y, M, C and B).

Beams for writing the latent images onto the photoconductor drums 58 (Y,M, C and B) are one or a plurality of beams in a sub-scanning directionon the photoconductor drums 58 which is (are) guided by mirrors 37Y,37M, 37C and 33B of the optical beam scanning device 1.

Laser beams LY, LM, LC and LB for the color components (possibly asynthesized beam of plural beams) are emitted onto the surfaces of thephotoconductor drums 58 (Y, M, C and B) between the charging devices 60(Y, M, C and B) and the developing devices 62 (Y, M, C and B) relatedwith the respective color components.

A paper cassette 70, which houses recording media, namely, the paper Ponto which the images formed by the image forming sections 50 (Y, M, Cand B) are transferred, is arranged below the transport belt 52.

A feed roller 72 is arranged at one end of the paper cassette 70 in avicinity of the tension roller 54. The feed roller 72 is formed into anapproximately half-moon shape, and feeds the paper P housed in the papercassette 70 one by one from the top.

A resist roller 74 is arranged between the feed roller 72 and thetension roller 54. The resist roller 74 matches a forward end of onepiece of paper P taken out from the cassette 70 with a forward end ofthe toner image formed on the photoconductor drum 58B of the imageforming section SOB (black).

An adsorption roller 76 is arranged substantially on an outer peripheryof the tension roller 54 via the transport belt 52 between the resistroller 74 and the first image forming section 50Y in a paper runningdirection in a vicinity of the tension roller 54. The adsorption roller76 provides predetermined electrostatic adsorptive power to one piece ofpaper P transported by the resist roller 74 at predetermined timing. Anaxial line of the adsorption roller 76 is parallel with an axial line ofthe tension roller 54.

Resist sensors 78 and 80 (since FIG. 1 is a front sectional view, onlythe backward sensor 80 is shown) are arranged substantially on an outerperiphery of the belt driving roller 56 via the transport belt 52 at oneend of the transport belt 52 in a vicinity of the belt driving roller56. The resist sensors 78 and 80 detect a position of the image formedon the transport belt 52 or the paper P transported by the transportbelt 52.

A transport belt cleaner 82 is arranged on the transport belt 52corresponding to the outer periphery of the belt driving roller 56. Thetransport belt cleaner 82 removes toner or waste of the paper P adheredto the transport belt 52.

A fixing device 84 is arranged in a direction where the paper Ptransported by the transport belt 52 is separated from the belt drivingroller 56 and is further transported. The fixing device 84 fixes thetoner image transferred onto the paper P to the paper P.

FIGS. 2 and 3 illustrates detailed structure of the multi-beam opticalscanning device to be used in the color image forming apparatus shown inFIG. 1. In FIG. 1, a pre-deflection optical system of the multi-beamoptical scanning device is omitted, but FIG. 2 shows the pre-deflectionoptical system. FIG. 2 illustrates developed reflection by means ofreflecting mirrors, mentioned later, that separate the deflected lightbeams into laser beams for the respective color components.

As shown in FIG. 2, the multi-beam optical scanning device 1 has onlyone light deflecting device 5 as a deflecting unit that deflects thelaser beams emitted from laser elements as light sources towards imagesurfaces arranged in predetermined positions, namely, predeterminedpositions of the photoconductive drums 58Y, 58M, 58C and 58B of the fourimage forming sections 50Y, 50M, 50C and 50B shown in FIG. 1 at apredetermined linear speed. In this specification, a direction where thelaser beam is deflected by the light deflecting device 5 is called as amain scanning direction.

The light deflecting device 5 has a polygon mirror 5 a where a flatmirror with a plurality of surfaces (for example, eight surfaces) isarranged into a regular polygon shape, and a motor 5 b which rotates thepolygon mirror 5 a at a predetermined speed. The polygon mirror 5 a isformed of aluminum, for example. Respective reflecting surfaces of thepolygon mirror 5 a are realized in such a manner that the polygon mirror5 a is cut along the sub-scanning direction as a surface including thedirection where the polygon mirror 5 a rotates, namely, the surfaceperpendicular to the main scanning direction, and a surface protectivelayer such as SiO₂ is deposited on a cut surface.

A post-deflection optical system is provided between the lightdeflecting device and the image surfaces. The post-deflection opticalsystem has first and second imaging lenses (so-called fθ lenses) 30 aand 30 b that give a predetermined optical property to the laser beamdeflected to the predetermined direction by the reflecting surface ofthe light deflecting device 5. The first and the second imaging lenses30 a and 30 b are designed cooperatively with each other so that theimage surfaces and the reflecting points on the polygon mirror surfacesestablish a schematically conjugate relationship in sub-scanningdirection. As a result, the first and the second imaging lenses 30 a and30 b prevent a fluctuation in the sub-scanning position on the imagesurfaces due to an influence of tilt of the reflecting surfaces in thepolygon mirror 5 a (tilt between angles and axial lines of the centeraxis of the reflecting surface.). For this reason, a positive power isprovided in the sub-scanning direction.

The first and the second imaging lenses 30 a and 30 b are cooperativewith each other so that the image surfaces and the reflecting points onthe reflecting surfaces establish the schematically conjugaterelationship in order to prevent the fluctuation in the sub-scanningdirection on the image surfaces due to the influence of the tilt of thereflecting surfaces of the polygon mirror 5 a (tilt between the anglesand the axial lines of the reflecting surfaces) For this reason, thefirst and the second imaging lenses 30 a and 30 b have the positivepower in the sub-scanning direction.

Further, as shown in FIG. 3, the post-deflection optical system hasfirst reflecting mirrors 33Y, 33M, 33C and 33B, second reflectingmirrors 35Y, 35M and 35C, and third reflecting mirrors 37Y, 37M and 37C.The laser beam LB for black component emitted from the second imaginglens 30 b of the post-deflection optical system is reflected by thefirst reflecting mirror 33B so as to be emitted to the photoconductordrum 58B. Laser beams LY, LM and LC for the other color componentsemitted from the second imaging lens 30 b are reflected by the firstreflecting mirrors 33Y, 33M and 33C, the second reflecting mirrors 35Y,35M and 35C, and the third reflecting mirrors 37Y, 37M and 37C,sequentially so as to be emitted to the photoconductor drums 58Y, 58Mand 58C.

The optical beam scanning device 1 has four light sources 3Y, 3M, 3C and3B including one or a plurality of laser elements that emit light beamsto be led to the photoconductor drums 58 (Y, M, C and B), respectively.Even when the light sources 3 (Y, M, C and B) emit a plurality of laserbeams including the laser elements, the laser beams from the lightsources are combined with an interval such that paired laser beams fromthe laser elements generally become one beam.

Pre-deflection optical systems 7 (Y, M, C and B), which adjust sectionalbeam spot shapes of the laser beams L (Y, M, C and B) from the lightsources 3 (Y, M, C and B) into predetermined shapes, are arrangedbetween the light sources 3 (Y, M, C and B) and the light deflectingdevice 5.

After predetermined convergence is given to the emanative laser beams L(Y, M, C and B) emitted from the light sources 3 (Y, M, C and B) byfinite focal lenses 9 (Y, M, C and B), the sectional beam shapes areadjusted into the predetermined shapes by stops (not shown in FIG. 2).Predetermined convergence is further given to the laser beams L (Y, M, Cand B) which pass through the stops only in the sub-scanning directionby glass cylinder lenses 11 (Y, M, C and B). The glass cylinder lenses11 (Y, M, C and B) are composed of, for example, BK7. The laser beams L(Y, M, C and B), thereafter, are synthesized into approximately oneoptical path (one in the main scanning direction, but incident angles tothe reflecting surface of the light deflecting device or positions areslightly different in the sub-scanning direction) by optical pathsynthesizing units 13 a, 13 b, 13 c and 13 d such as reflecting mirrorsor beam splitters. The laser beams L (Y, M, C and B) are guided to theone reflecting surface of the light deflecting unit 5.

The finite focal lenses 9 (Y, M, C and B) are composed of a single lensin which, for example, an UV curing plastic a spherical lens, not shown,is laminated with a spherical glass lens or an a spherical glass lens.

This embodiment is characterized in that an environment changecompensating optical element having the function for compensatingdisplacement of the sub-scanning direction due to an environment change(for example, temperature change) is provided onto the common opticalpath (approximately combined one optical path) for the laser beams L (Y,M, C and B) before reaching the light deflecting device 5. A free-formsurface lens formed by plastic such as COP (cycloolefin polymer) or PMMA(polymethyl methacryl) is applied to the environment change compensatingoptical element 15. The environment change compensating optical elementhas a negative power at least in a sub-scanning direction.

FIGS. 4A and 4B are conceptual explanatory diagrams of the environmentchange compensating optical element 15, FIG. 4A is a diagram in the casewhere the environment change compensating optical element is notprovided, and FIG. 4B is a diagram in the case where the environmentchange compensating optical element 15is provided. Further, FIGS. 4A and4B illustrate the optical path in the sub-scanning direction where thereflection on the reflecting surface 5R of the light deflecting deviceis replaced by transmission surface. In FIGS. 4A and 4B, only the two offour laser beams for the color components (in this case, they aretentatively the laser beams LY and LB) are shown, and the first and thesecond imaging lenses (fθ lenses) 30 a and 30 b in the post-deflectionoptical system are regarded as one lens having the function equivalentto the function in the case where two lenses are synthesized.

When the temperature change is taken into consideration, a glass lens ismore preferable than a plastic lens as the lenses applied to the device.The first and the second imaging lenses (fθ lenses) 30 a and 30 b,however, need to secure sufficient length in the main scanningdirection, and thus the plastic lenses are adopted after their weightand cost are taken into consideration.

In the case where the environment change compensating optical element isnot provided, the glass cylinder lenses 11Y and 11B are hardlyinfluenced by the temperature change. For this reason, the laser beamsLY and LB which pass through the glass cylinder lenses 11Y and 11B arehardly influenced by the temperature change, so as to advance thesimilar path. When temperature rises, however, the first and the secondimaging lenses (fθ lenses) 30 a and 30B composed of the plastic lensesare influenced by the state that as the dimension of the members becomelarger and the refractive index become smaller. As a result, thepositive power is reduced, and when the laser beams reach the imagingsurfaces (photoconductor drums 58Y and 58B), great displacement occursin the sub-scanning direction. The paths shown by alternate long andshort dash lines in FIG. 4A represent this case.

On the contrary, when the environment change compensating opticalelement is provided, the laser beams LY and LB which pass through theglass cylinder lenses 11Y and 11B pass through the environment changecompensating optical element before they reach the first and the secondimaging lenses (fθ lenses) 30 a and 30 b composed of the plastic lenses.When the plastic lenses having the negative power are adopted as theenvironment change compensating optical element 15, the environmentchange compensating optical element functions so as to narrow theintervals between the laser beams on the reflecting surface 5R of thelight deflecting device when the temperature rises. That is to say, theenvironment change compensating optical element functions to an oppositedirection to the direction where the first and the second imaging lenses(fθ lenses) 30 a and 30 b composed of the plastic lenses function whenthe temperature rises. As a result, it functions so as to narrowemitting positions of the imaging surfaces (photoconductor drums 58Y and58B) of the laser beams LY and LB. When the power and the incident angleof the environment change compensating optical element are set, anemitting position change amount can be set freely and can be set to beapproximately equal before and after the rise of the temperature.

A study is conducted on how to set the necessary compensating function(lens characteristic of the environment change compensating opticalelement 15) of the environment change compensating optical element 15.It is necessary to understand image shift and color shift due to theenvironment change (temperature change) of the entire device in order toset the necessary compensating function.

The study is conducted on the case of the two photoconductor drums shownin FIG. 5 (the two photoconductor drums for the yellow and blackcomponents are tentatively explained).

The interval between the laser beams LY and LB to the two photoconductordrums 58Y and 58B is designated by L, a radius of the photoconductordrums 58Y and 58B is designated by rd, an angle between an exposingpoint and a transfer point on the photoconductor drums 58Y and 58B isdesignated by α, a rotating speed of the photoconductor drums 58Y and58B is designated by ωd, a shaft radius of the belt driving roller 56 isdesignated by rs, and an angular velocity of the belt driving roller 56is designated by ωs. The equation (1) is established at the time ofstandard, and in order to overlap the images on one place of paper,exposure needs to be carried out with time difference T expressed by theequation (2) being provided between the timing of the writing with thelaser beam LY and the timing of the writing with the laser beam LB.rd×ωd≈rs×ωs=v  (1)T=L/v  (2)(a) Influence of Fluctuation in the Emitting Positions of the LaserBeams

When the standard sate shown in FIG. 5 is changed into a state shown inFIG. 6 that the interval of the laser beams LY and LB shifts only byΔLH, the time at which the image written by the laser beam LB reachesthe transfer point is delayed only by time ΔTH expressed by the equation(3). This means that the image by the laser beam LB shifts to the rearside (the sub-scanning direction: the right side in FIG. 6) only by adistance expressed by the equation (4).ΔTH≈ΔLH/v  (3)v×ΔTH≈ΔLH  (4)(b) Influence of Fluctuation in the Positions of the PhotoconductorDrums

When the standard state shown in FIG. 5 is changed into a state shown inFIG. 7 that the distance between the two photoconductor drums 58Y and58B is shifted only by ΔLF, the time at which the image written by thelaser beam LB reaches the transfer point is delayed only by time ΔTFexpressed by the equation (5). This means that the image by the laserbeam LB is shifted to the front side (the sub-scanning direction: theleft side in FIG. 7) only by a distance expressed by the equation (6).When the distance between the two photoconductor drums 58Y and 58B ischanged only by ΔLF, the transfer point of the image with the laser beamLB changes only by ΔLF. Totally, the image by the laser beam LB isshifted to the front side (the sub-scanning direction: the left side inFIG. 7) only by an absolute value expressed by the equation (7). “−” inthe equation (7) designates a shift direction, and the shift to theright side is designated by “+”.ΔTF≈−ΔLF/v  (5)v×ΔTF≈−ΔLF  (6)−2×ΔLF  (7)(c) Influence of Fluctuation in the Shaft Radius

When the shaft radius of the belt driving roller 56 becomes large onlyby Δrs, a linear moving speed (v) of the belt driving roller 56 becomesfaster only by Δrs×ωs. For this reason, the advancing distance of thebelt (the medium on the belt) for time T becomes large by a valueobtained by the equation (8). This means that the image by the laserbeam LB is shifted to the rear side (the sub-scanning direction: theright side in FIGS. 6 and 7) only by the value obtained by the equation(8).Δrs×ωs×T=L×Δrs/rs  (8)

The causes that bring the image shift in the sub-scanning direction arethree kinds of fluctuations described in (a) to (c), and when there aretwo or three of fluctuations at the same time, the image by the laserbeam LB is shifted from the standard state by a value obtained by theequation (9) according to the equations (4), (7) and (8).ΔLH−2×ΔLF+L×Δrs/rs  (9)

A synthesized linear expansion coefficient (synthesized thermalexpansion coefficient) of a member that houses the optical system suchas the optical beam scanning device 1 of the embodiment (hereinaftercalled housing) is designated by αH, a synthesized linear expansioncoefficient (synthesized thermal expansion coefficient) of a member thatsupports the photoconductor drums 58Y and 58B (hereinafter called aframe) is designated by αF, a synthesized linear expansion coefficient(synthesized thermal expansion coefficient) of the belt driving roller(shaft) 56 is designated by αS, and temperature rise is designated by t.At this time, the three fluctuations ΔLH, ΔLF and Δrs can be expressedby the equations (10) to (12) respectively.ΔLH=αH×L×t  (10)ΔLH=αF×L×t  (11)Δrs=αS×rs×t  (12)

When the equations (10) and (12) are applied to the equation (9), theequation (13) is obtained. The equation (13) expresses that when thetemperature rises by t, the image by the laser beam LB is influenced bythe synthesized linear expansion coefficients (synthesized thermalexpansion coefficients) of the respective sections so as to be shiftedto the rear side (the sub-scanning direction: the right side in FIG. 5)only by the value obtained by the equation (13) from the standard stateshown in FIG. 5.αH×L×t−2×αF×L×t+L×αS×rs×t/rs=(αH−2×αF +αS)×(L×t)=Δ  (13)

According to the equation (13), it is found that when the temperaturerises by t, the emitting position of the laser beam LB may be moved fromthe position before the rise to an opposite direction only by the sameamount as the absolute amount Δ expressed by the equation (13) (−Δ). Theabove explanation is given assuming that only the image by the laserbeam LB changes, but both the emitting positions of the laser beams LBand LY change. The equation (13), therefore, expresses that when thetemperature rises by t, the pitch between the laser beams LB and LY ischanged only by −Δ. That is to say, the emitting positions of thephotoconductor drums for the laser beams LB and LY are not fixed but thepitch between the emitting positions of the laser beams LB and LY isrelatively moved only by −Δ which is opposite to the amount expressed bythe equation (13). As a result, even if the ambient environment changes(particularly the temperature change), a plurality of images are notdisplaced (precise color registration is maintained).

For simplification of the explanation, the case of the two laser beamsLB an LY is explained, but like the above embodiment, the similarfunction is applied to the case of the four laser beams LY, ML, LC andLB.

Only when the pitch between the beams in the sub-scanning directionexpands only by αH×BP×t (here, BP is the gap between the beam positionsin the sub-scanning direction on the image surfaces at the time ofdeveloping the optical path reflection from the deflecting surface tothe image surfaces), the expansion of the optical system housing is justthe same as the fluctuation in the gap of the laser beams from thehousing.

For this reason, the beam positions of the surfaces to be scanned(corresponding to the surfaces of the photoconductor drums) at the timeof developing the reflecting mirrors are shifted only by Δ′ expressed bythe equation (13′), occurrence of a shift of color overlapping due totemperature change can be prevented. As a result, an amount of the colorshift without registration control can be suppressed, or the timeinterval of the registration control can be enlarged.−(αH−2×αF+αS)×(L×t)+αH×BP×t=Δ′  (13′)

The environment change compensating optical element 15, as explainedwith reference to FIG. 4B, suppresses the displacement in thesub-scanning direction on the surface to be scanned at the time oftemperature change, but cannot completely suppress the shift of coloroverlapping by only setting the displacement of the beams to 0. For thisreason, when the temperature rises by t, the characteristic and theshape of the environment change compensating optical element 15 areselected so that the beam positions on the surface to be scanned at thetime of developing the reflecting mirrors shift only by−(αH−2×αF+αS)×(L×t)+αH×BP×t. As a result, the occurrence of the shift ofcolor overlapping (error of color registration) due to temperaturechange can be prevented, and the amount of the color shift (error ofcolor registration) without the registration control is suppressed orthe time interval of the registration control can be increased.

In general, since the frame and the shaft are formed by iron materials,and the housing is formed of aluminum or plastic, αH>αF≈αS isestablished. For this reason, −(αH−2αF+αS)×L<0 is obtained. As a result,when the temperature rises, it is desirable that the increase in theinterval in the sub-scanning direction is smaller than αH×BP×t as theoptical system.

The optimal optical power arrangement including the environment changecompensating optical element 15 is carried out, so that the opticalsystem, which suppress the fluctuation in the beam positions in thesub-scanning direction and reduces temperature dependency of the imagingsurfaces in the sub-scanning direction, can be provided.

(A-1) First Concrete Example of the Embodiment

The optical beam scanning device and the image forming apparatus of theabove-mentioned embodiment are explained according to the first concreteexample.

In the first concrete example, the material of the optical systemhousing is an aluminum die cast with linear expansion coefficient ofαH=2.1×10⁻⁵, and the material of the frame for defining the intervalsbetween the photoconductor drums is an aluminum die cast with linearexpansion coefficient of αF=2.1×10⁻⁵. The material of the transfer beltdriving shaft is free-cutting steel with linear expansion coefficient ofαS=1.15×10⁻⁵, and the interval L between the photoconductor drums (forblack and yellow) on both ends is 225 mm.

In the case where temperature rises by 15° C. (t=15), the ideal value Δ′as a change amount of the distance between the beams on both ends in thesub-scanning direction can obtain 0.032 according to the equation (13′)(this means that when the emitting positions in the sub-scanningdirection do not shift at all even if temperature changes, the shift ofthe color overlapping of 32 μm occurs).

FIGS. 8 to 11 are explanatory diagrams of data about the optical beamscanning device 1 which can realize approximately 32 μm as the changemount Δ′ of the distance between the beams on both the ends in thesub-scanning direction when the temperature rises by 15° C.

FIGS. 8 to 11 illustrate the case where when a diameter of an inscribedcircle of the polygon mirror 5 a is 40.0 mm, the main scanning directionis a y direction, the sub-scanning direction is a z direction, and theoptical axis direction is an x direction (light propagates to “+” inpre-deflection optical system, and propagates to “−” in post-deflectionoptical system), the rotating center position of the polygon mirror 5 ais such that the y direction is 17.2 mm and the z direction is 10.1 mmon a local coordinate system of the reflecting surfaces of the polygonmirror 5 a. An definitional equation of the lens surfaces in thesedrawings is the equation (14), and in this concrete example, ay is 1 andaz is 1. $\begin{matrix}{x = {\frac{{{cuy} \times y^{2}} + {{cuz} \times z^{2}}}{1 + {\sqrt{1 - {ay}} \times {cuy}^{2} \times y^{2}} - {{az} \times {cuz}^{2} \times z^{2}}} + {\sum{a_{lm} \times y^{1} \times z^{m}}}}} & (14)\end{matrix}$

FIG. 8 illustrates curvature and the interval (TH) on the optical axeson the surfaces of the optical elements, and refractive index of theoptical elements. The distances between the adjacent surfaces of theoptical elements are common among the laser beams LY (in the drawing,RAY 1, and the same is applied to the other ones), LM (RAY2), LC (RAY3)and LB (RAY4) when the number is written in common row, and aredifferent among the laser beams LY (RAY1), LM (RAY2), LC (RAY3), and LB(RAY4) when the number is written in ray1 ˜ray4 row. FIG. 8 describesdata about the emitting surfaces and thereafter of the finite focallenses 9Y, 9M, 9C and 9B, and the distances between the finite focallenses 9Y, 9M, 9C and 9B and the imaging positions are 1159.4 mm, 1106.0mm, 1136.0 mm and 1202.3 mm, respectively.

FIG. 9 shows eccentricity (shift, de-center) and tilt of the opticalelements on the local coordinate system, and the optical elements arearranged with eccentricity and the tilt shown in FIG. 9. In FIGS. 8 and9, the surface Nos. are the same.

In FIGS. 8 and 9, the surface No. “2” shows a curved surface side of theglass cylinder lenses 11 (Y, M, C and B), and the surface No. “3” showsa plane side. The distance in the surface No. “4” represents a commondistance up to the incident surface of the optical elements in thesurface No. “5” among the laser beams LY (RAY1), LM (RAY2), LC (RAY3),and LB (RAY4). The distance described on the surface No. “3” representsa difference between the common distance and the actual distance foreach laser beam. The surface Nos. “5” and “6” show the incident surfaceand the emission surface of the beam splitter as the optical pathsynthesizing unit (13 d), respectively.

The surface Nos. “7” and “8” show the incident surface and the emissionsurface of the plastic lens as the environment change compensatingoptical element 15. A curved surface polynomial coefficient of theincident surfaces is shown in FIG. 10A, and a curved surface polynomialcoefficient of the emission surfaces is shown in FIG. 10B. As is clearfrom FIGS. 8, 10A and 10B, the environment change compensating opticalelement 15 has a curved surface in the main scanning direction, and hasa negative power in order to compensate temperature characteristic ofthe post-deflection optical system having the positive power in the mainscanning direction. The emitting position shift of the image surfacesdue to temperature change which is smaller than that in the sub-scanningdirection occurs also in the main scanning direction, and the curvedsurface in the main direction compensates this shift. FIG. 11 shows aparaxial power of the environment change compensating optical element 15(plastic lens), and it has a negative power in the sub-scanningdirection (and the main scanning direction).

The surface Nos. “9” and “10” show the incident surface and the emissionsurface of a cover glass (not shown in FIG. 2) which covers the polygonmirror 5 a on the pre-deflection side. The surface No. “11” shows thedeflection surface, and the surface Nos. “12” and “13” show the incidentsurface and the emission surface of the cover glass on thepost-deflection side.

The surface Nos. “14” and “15” show the incident surface and theemission surface of the plastic lens as the first imaging lens 30 a, acurved surface polynomial coefficient of the incident surface is shownin FIG. 10C, and a curved surface polynomial coefficient of the emissionsurface is shown in FIG. 10D. The surface Nos. “16” and “17” show theincident surface and the emission surface of the plastic lens as thesecond imaging lens 30 b, a curved surface polynomial coefficient of theincident surface is shown in FIG. 10E, and a curved surface polynomialcoefficient of the emission surface is shown in FIG. 10F.

The surface No. “18” shows the incident surface of the cover glass (notshown in FIG. 2) with respect to the entire optical beam scanning device1, and the surface No. “19” shows the emission surface. The distancedescribed in the surface No. “20” shows the common distance up to theimage surfaces (the surfaces of the photoconductor drums) among thelaser beams LY (RAY1), LM (RAY2), LC (RAY3), and LB (RAY4), and thedistance described in the surface No. “19” shows a difference betweenthe common distance and the actual distances for each laser beam.

When the optical beam scanning device 1 of the concrete example isapplied, as shown in FIG. 12, the laser beam LY (RAY1; yellow) and thelaser beam LB (RAY4; black) move to a direction where they spread 25 μmwider than the housing expansion due to the temperature rise of 15° C.That is to say, the laser beams move to the direction where theregistration shift amount of 32 μm when the emitting positions of thelaser beams do not move is canceled. For this reason, even if thetemperature rises by 15° C., the yellow and black overlapping shiftsonly by 7 μm.

Similarly, the relationship between the laser beams LM (RAY2; magenta)and LB (RAY4; black) is such that L=75×2=150, and the registration shiftamount when the light beams do not move is 22 μm. Since the relativedistance between both the laser beams, however, moves 16 μm to thecanceling direction, even if temperature rises by 15° C., the magentaand black overlapping shifts only by 6 μm. The relationship between thelaser beams LC (RAY3; cyan) and LB (RAY4; black) is such that L=75, andthe registration shift amount when the beams do not move is 11 μm. Sincethe relative distance of both the laser beams, however, moves by 14 μ tothe canceling direction, even if temperature rises by 15° C., the cyanand black overlapping shifts only by 3 μm.

Further, a defocus change amount in the main scanning direction and thesub-scanning direction is suppressed to not more than 0.3.

(A-2) Second Concrete Example of the Embodiment

The second concrete example of the optical beam scanning device and theimage forming apparatus according to the embodiment are explained below.

In the second concrete example, the material of the optical systemhousing is carbon fiber reinforced polycarbonate resin with linearexpansion coefficient of αH=2.25×10⁻⁵, and the material of the framewhich defines the intervals between the photoconductor drums iscold-rolled steel plate with linear expansion coefficient ofαF=1.2×10⁻⁵. The material of the transfer belt driving shaft isstainless steel with linear expansion coefficient of αS=1.04×10⁻⁵, andthe interval L between the photoconductor drums on both ends (for blackand yellow) is 225 mm.

In the case where temperature rises by 15° C. (t=15), the ideal value Δ′as a change amount of the distance between the beams on both ends in thesub-scanning direction can obtain −0.030 according to the equation (13′)(this means that when the emitting positions in the sub-scanningdirection do not shift at all even if temperature changes, the shift ofthe color overlapping of 30 μm occurs).

In the second concrete example, a member which defines heights of thelight source (LD), the limited focal lenses and the glass cylinderlenses of the pre-deflection optical system is separated from thehousing that holds all the entire optical parts. Concretely, this memberis made of a metal matrix composite (ceramic reinforcement is used as afiller so as to be combined with metal matrix). The metal matrixcomposites with different thickness are sandwiched between the opticalhousing, the light sources (LD), the limited focal lenses and the glasscylinder lenses, so that the positions in the sub-scanning directionsare made to be different.

The post-deflection optical system of the second concrete example is thesame as the post-deflection optical system of the first concreteexample.

FIGS. 13 to 16 are diagrams corresponding to FIGS. 8 to 11 according tothe first concrete example, and show only the pre-deflection opticalsystem.

In the second concrete example, as shown in FIG. 17, when thetemperature rises by 15° C., the laser beams LY (RAY1; yellow) and LB(RAY4; black) move to a direction where they become 5 μm smaller thanthe direction in the case of the housing expansion. That is to say, thebeams LY and LB move to the direction where the registration shiftamount of 30 μm in the case where the laser beam emitting positions donot move is canceled. For this reason, even when temperature rises by15° C., the yellow and black overlapping shifts only by 25 μm (thisvalue is large, but when the plastic lens with negative power is notprovided to the pre-deflection optical system, as mentioned later, theshift is 114 μm, and thus 25 μm is very smaller than 114 μm).

In the second concrete example, the defocus change amount in the mainscanning direction and the sub-scanning direction is suppressed to notmore than 0.3.

In the second concrete example, when temperature rises, the intervals ofthe beams on the surfaces to be scanned can be small.

FIGS. 18 to 20 illustrate data about the optical systems in acomparative example. In the comparative example, the plastic lens is notprovided as the environment change compensating optical element 15. Thepost-deflection optical system in the comparative example is similar tothat in the second concrete example.

FIG. 18 is a diagram corresponding to FIG. 13 in the second concreteexample, FIG. 19 is a diagram corresponding to FIG. 14 in the secondconcrete example, and FIG. 20 is a diagram corresponding to FIG. 16 inthe second concrete example.

In the comparative example, as shown in FIG. 21, the laser beams LY(RAY1; yellow) and the laser beam LB (RAY4; black) move to the directionwhere they spread 84 μm when temperature rises by 15° C.

In the combination example of the materials of the housing, the framemember that defines the intervals between the photoconductor drums andthe transfer belt driving shaft in the first concrete example, theregistration shifts 84 μm with respect to the shift of 32 μm in the casewhere the laser beam emitting positions do not move. For this reason,when temperature rises by 15° C., the yellow and black overlappingshifts by 52 μm.

In the combination example of the materials of the housing, the framemember that defines the intervals between the photoconductor drums andthe transfer belt driving shaft in the second concrete example, theregistration shifts by 84 μm to the opposite direction in addition tothe registration shift amount of 30 μm in the case where the beams donot move. For this reason, when temperature rises by 15° C., the yellowand black overlapping shifts by 114 μm.

It is clear that the provision of the environment change compensatingoptical element 15 (plastic lens) can suppress the color overlapping dueto the temperature change.

Further, from the comparison between FIGS. 21 and 12 and the comparisonbetween FIGS. 21 and 17, the defocus change amount in the main scanningdirection and the sub-scanning direction in the comparative example islarger than that in the first and the second concrete examples.

Even when the beam waist positions in the sub-scanning direction changesdue to temperature change in the post-deflection optical system, theenvironment change compensating optical element 15 (plastic lens) isprovided to the pre-deflection optical system, so that the imagingsurfaces are shift to the opposite direction to the direction where theshift occurs in the post-deflection optical system and correction can bemade. As a result, the shift of the color overlapping in thesub-scanning direction can be suppressed, and the color shift amountwithout the registration control can be suppressed, or the timeintervals of the registration control can be increased.

Not only in the sub-scanning direction but also in the main scanningdirection, the environment change compensating optical element 15(plastic lens) is provided to the pre-deflection optical system, so thatthe similar effect can be produced in order to prevent defocus due toenvironment change.

(B) Another Embodiment

The above embodiment explains the image forming apparatus wheremaximally four images are overlapped with one another, but the presentinvention can be applied to an image forming apparatus where the maximumnumber of images to be overlapped is smaller or larger than four.Further, the color components of the images to be overlapped are notlimited to different color components.

The above embodiment explains that all the laser beams are guided ontothe one surface of the polygon mirror, but the present invention can besuitably applied to an apparatus which uses the two surfaces of thepolygon mirror.

The above embodiment explains the environment change compensatingoptical element 15 which is the lens (plastic lens as one example)having the negative power, but another kind of optical element havingsimilar incident and emission characteristics may be used. For example,transmitting or reflecting diffraction grating with non-uniform pitchcan be used.

Further, the above embodiment explains that the compensating function ofthe environment change compensating optical element 15 is determinedaccording to the equation (13′), but the equation (13′) does not have tobe considered for the compensating function. For example, when thetemperature rise in the scanning optical unit is larger than the outsideof the unit, as explained with reference to FIG. 4B, the compensatingfunction may be determined so as to have temperature dependency oppositeto that of the imaging lenses (first and second imaging lenses). That isto say, the compensating function does not have to be determined takingthe linear expansion coefficient of the materials of the opticalhousing, the frame which defines the intervals between thephotoconductor drums, and the transfer belt driving shaft intoconsideration.

The above embodiment explains the member which compensates the imageshift according to the equation (13) is mainly composed of theenvironment change compensating optical element 15 provided to theposition common among the plural laser beams in the pre-deflectionoptical system. The member, which compensates the image shift obtainedby the equation (13) by means of movement of opposite positive ornegative amount, may be provided on the optical paths of some of theplural laser beams. For example, the environment change compensatingoptical element 15may be provided to positions obtained by synthesizingthe two optical paths.

The above embodiment explains that the linear expansion coefficients ofthree materials of the optical housing, the frame which defines theintervals between the photoconductor drums and the transfer belt drivingshaft are taken into consideration, but a number of the materials to beconsidered may be smaller or larger than three.

1. An optical beam scanning device, comprising a plurality of opticalelements that are arranged on a housing and give a plurality of scanninglines to a plurality of photoconductor drums with an interval L, whereinwhen linear expansion coefficients of the housing, a frame for locatingthe photoconductor drums and a shaft for driving a belt or on arecording medium carried on the belt on which images developed on thephotoconductor are overlapped are designated by αH, αF and αS,respectively, and when an interval between the beams positions onsurfaces to be scanned in a sub-scanning direction at the time ofdeveloping an optical path reflection by mirrors from a deflectingsurface to the surfaces to be scanned is designated by BP,characteristics are selected so that intervals of the beams in thesub-scanning direction are shifted only by −(αH−2×αF+αS)×L×αH×BP perunit temperature.
 2. The optical beam scanning device according to claim1, wherein the optical elements include: a single light deflectingdevice; an optical element of a post-deflection optical system includinga first optical element for imaging reflected light beams from the lightdeflecting device on the surfaces to be scanned for respective beams;and an optical element of a pre-deflection optical system which includesa second optical element provided in a position where the light beamsfrom the light sources enter with distance in sub-scanning direction andhaving a positive or negative power opposite to a power of the firstoptical element in the sub-scanning direction, and allows the lightbeams from the light sources to enter the light deflecting device.
 3. Animage forming apparatus, comprising: a plurality of photoconductors; aframe that locating the photoconductors; a housing; a belt on whichimages developed on the photoconductors are overlapped; a shift thatdrives the belt; and a plurality of optical elements which are arrangedon the housing, provides a plurality of scanning lines to thephotoconductor with an interval L, wherein when linear expansioncoefficients of the housing, the frame and the shaft are designated byαH, αF and αS, respectively, and intervals between beam positions onsurfaces to be scanned in a sub-scanning direction at the time ofdeveloping optical path reflection by mirrors from a deflecting surfaceto the surfaces to be scanned is designated by BP, characteristics areselected so that intervals of the beams in the sub-scanning directionare shifted only by −(αH−2×αF+αS)×L+αH×BP per unit temperature.